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arXiv · 1007.0171

Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems

J. -R. Chazottes·P. Collet
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Abstract

We study the number of visits to balls B_r(x), up to time t/mu(B_r(x)), for a class of non-uniformly hyperbolic dynamical systems, where mu is the SRB measure. Outside a set of `bad' centers x, we prove that this number is approximately Poissonnian with a controlled error term. In particular, when r-->0, we get convergence to the Poisson law for a set of centers of mu-measure one. Our theorem applies for instance to the H\'enon attractor and, more generally, to systems modelled by a Young tower whose return-time function has a exponential tail and with one-dimensional unstable manifolds. Along the way, we prove an abstract Poisson approximation result of independent interest.

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J. -R. Chazottes, P. Collet. 2010-07-01. Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems. https://arxiv.org/abs/1007.0171

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